I mainly asked because many feel that it was Cat freeing Jaime which caused Robb's death. What's your opinion about it? For that matter, do you think that Cat's actions were foolish and entirely motivated by emotion?

Well, I showed you her actions and let you see the thoughts processes that led up to them. Beyond that, I will leave the interpertations to my readers.

"The castle is so large it requires an army to hold it" according to Ser Aenys Frey in ACOK. Was he mistaken?

Well, not mistaken, but perhaps overstating the case. Still, the castle walls were extensive enough to require a much larger garrison than most actual medieval castles did in the real world sieges.

And how on earth could Tywin expect a sellsword company to be loyal enough to sit out a prolongued siege? Not to mention that Lorch and Hoat were known enemies...

Lorch's men were not sellswords, and Hoat's were assigned to plunder, foraging, and terror, three of their favorite things. Lord Tywin did perhaps underestimate the extent of their emnity (he had other things on his mind), and he did not anticipate Roose Bolton making such a generous offer to the goat... or the trickery that not the northmen "captives" inside the castle.

Would you by any chance consider writing a "Rains of Castamere" story from Tywin's POV ;)?